The Initial-Final Mass Relation of White Dwarfs: A Tool to Calibrate the Third Dredge-Up

The initial mass-final mass relationship (IFMR) of white dwarfs (WD) represents a crucial benchmark for stellar evolution models, especially for the efficiency of mixing episodes and mass loss during the asymptotic giant branch (AGB) phase. In this study, we argue that this relation offers the opportunity to constrain the third dredge-up (3DU), with important consequences for chemical yields. The results are discussed in light of recent studies that have identified a kink in the IFMR for initial masses close to 2 M-circle dot. Adopting a physically-sound approach in which the efficiency lambda of the 3DU varies as a function of core and envelope masses, we calibrate lambda in solar-metallicity TP-AGB models in order to reproduce the final masses of their WD progeny, over the range of initial masses 0.9 <= M-i/M-circle dot <= 6. In particular, we find that in low-mass stars with 1.4 less than or similar to M-i/M-circle dot less than or similar to 2.0 the efficiency is small, lambda <= 0.3, it steeply rises to about lambda similar or equal to 0.65 in intermediate-mass stars with 2.0 <= M-i/M-circle dot <= 4.0, and then it drops in massive TP-AGB stars with 4.0 less than or similar to M-i/M-circle dot <= 6.0. Our study also suggests that a second kink may show up in the IFMR at the transition between the most massive carbon stars and those that are dominated by hot-bottom burning.